HEADPHONES ADVANTAGES
Can block Traffic, Raging Sea, Children, Wind, or other distracting noises - especially if you have noise cancelling.
They stay on better (unless you are in the bush)
Keep your ears warm
EARPHONES ADVANTAGES
Compact & lighter when travelling.
Waterproof option is no more expensive (I paid $20)
Use less power - more battery for detecting time.
Easy to keep a spare in your pocket - just in case.
Some models hook around ears to help them stay in place.